(Back to the tutorial on rationalizing den. and num. of radical expressions )

Intermediate Algebra
Answer/Discussion to Practice Problems
on Rationalizing Denominators and Numerators 
of Radical Expressions


 

Answer/Discussion to 1a


 
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

 
Since we have a square root in the denominator,  we need to multiply by the square root of an expression that will give us a perfect square under the square root in the denominator. 

So in this case, we can accomplish this by multiplying top and bottom by the square root of 11:

 

*Mult. num. and den. by sq. root of 11
 
 

*Den. now has a perfect square under sq. root
 

 
Step 2: Make sure all radicals are simplified

AND

 
Step 3: Simplify the fraction if needed.

 

 
 
 

*Sq. root of 121 is 11
 

 

 
(return to problem 1a)

 


 

Answer/Discussion to 2a


 
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the numerator.

 
Since we have a cube root in the numerator,  we need to multiply by the cube root of an expression that will give us a perfect cube under the cube root in the numerator. 

So in this case, we can accomplish this by multiplying top and bottom by the cube root of :

 

 

*Mult. num. and den. by cube root of 
 
 

*Num. now has a perfect cube under cube root

 

 
Step 2: Make sure all radicals are simplified

AND

 
Step 3: Simplify the fraction if needed.

 

 

*Cube root of 125 y cubed is 5y

 

 
(return to problem 2a)

 


 

Answer/Discussion to 3a


 
Step 1: Find the conjugate of the denominator.

 
In general the conjugate of a + b is a - b and vice versa.

So what would the conjugate of our denominator be?

It looks like the conjugate is .

 
Step 2: Multiply the numerator and the denominator of the fraction by the conjugate found in Step 1 .

 

*Mult. num. and den. by conjugate of den.
*Product of the sum and diff. of two terms
 
 

 

 
Step 3: Make sure all radicals are simplified

AND

 
Step 4: Simplify the fraction if needed.

 
No simplifying can be done on this problem so the final answer is:


 
(return to problem 3a)

 

(Back to the tutorial on rationalizing den. and num. of radical expressions )

All contents copyright (C) 2001 - 2008, WTAMU and Kim Seward. All rights reserved.
Last revised on Jan. 8, 2002 by Kim Seward.